A113107 Number of 5-tournament sequences: a(n) gives the number of increasing sequences of n positive integers (t_1,t_2,...,t_n) such that t_1 = 1 and t_i = 1 (mod 4) and t_{i+1} <= 5*t_i for 1

1, 1, 5, 85, 4985, 1082905, 930005021, 3306859233805, 50220281721033905, 3328966349792343354865, 978820270264589718999911669, 1292724512951963810375572954693765

Offset: 0

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn

Comments

Equals column 0 of triangle A113106 which satisfies recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k), where A113106^5 is the matrix 5th power.

Examples

			The tree of 5-tournament sequences of descendents
of a node labeled (1) begins:
[1]; generation 1: 1->[5]; generation 2: 5->[9,13,17,21,25]; ...
Then a(n) gives the number of nodes in generation n.
Also, a(n+1) = sum of labels of nodes in generation n.
		

Links

• M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.

Crossrefs

Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113109, A113111, A113113.

Programs

PARI

{a(n)=local(M=matrix(n+1,n+1));for(r=1,n+1, for(c=1,r, M[r,c]=if(r==c,1,if(c>1,(M^5)[r-1,c-1])+(M^5)[r-1,c]))); return(M[n+1,1])}